To illustrate the problem of thermal management, reference is made to the computer and microelectronics industry. Progress in VLSI (Very Large Scale Integration) semiconductor technology is often discussed in terms of Moore's Law, which in its most common definition predicts a doubling of the number of transistors per CPU (Central Processing Unit) every 18 months. In 1971, Intel introduced the “4004” processor, which contained 2,300 transistors and ran at a clock speed of 740 kHz. By 2006, processors with over a billion transistors and clock speeds in excess of 3 GHz had become commercially available. Many such modem CPUs generate well in excess of 100 W of waste heat. Continued progress in advancing CPU capability is now seriously hampered by the problem of thermal management. The limitations of state-of-the-art thermal management technology fall well short of what is required to continue along the growth curve of Moore's Law, a situation that has been termed the “thermal brick wall” problem.
An example of a current state of the art CPU cooler is shown in FIG. 1, which includes a finned metal heat sink 1 with a flat bottom surface (to facilitate making a low thermal-resistance connection to a thermal load), and an axial fan 2 for generating an airflow that impinges on the heat sink fins. The heat sink 1 has a plurality of fins to increase the heat-exchanging surface area and is made from a material with high thermal conductivity, such as aluminum. The choice of material used for the metal heat sink may also reflect other requirements, such as the need to make the heat sink light-weight, low-cost, easy to manufacture (e.g., the use of an alloy with good mechanical forming properties), etc. Also included are fastening means 3 and 4 for securing fan 2 to heat sink 1.
In the vast majority of desktop and laptop computers, the CPU is mounted in direct thermal contact with a CPU cooler such as that shown in FIG. 1, or connected indirectly through a heat extraction device such as a heat pipe. The state of the art for electronics thermal management technology may be further illustrated with reference to art covered by U.S. Patent Classification Classes and Subclasses 165/121, 165/104.33 and 361/697 and particularly to U.S. Pat. Nos. 7,349,212, 7,304,845, 7,265,975, 7,035,102, 6,860,323, 6,356,435 and published U.S. Patent Publication Numbers 2004/0109291, 2005/0195573 and 2007/0041158.
Early on in the semiconductor industry, component designers realized that many devices such as power transistors required some form of thermal management in order to maintain adequate device temperature operating margins (cf. U.S. Pat. No. 5,736,787). To solve this problem, such components were typically mounted in direct contact with a finned metal heat sink. Such finned heat sinks relied primarily on natural convection to circulate air through the cooling fins. Eventually it became routine to use a fan for assisting air movement over and around the heat sink to improve the rate and efficiency of heat extraction from the heat sink. Over time, heat sinks for electronics cooling grew larger in size, incorporated larger numbers of fins, and used ever more elaborate fin geometries in an attempt to further improve heat exchange between the heat sink and surrounding air. This “heat-sink-plus-fan” architecture (see FIG. 1) still represents the state of the art in air-cooled heat exchanger technology (cf. Incropera F. P., Dewitt D. P., Bergman, T. L. and Levine, A. S., Fundamentals of Heat and Mass Transfer, 6th Edition, John Wiley & Sons, New York, 2007).
Until the mid 1990s, relatively little attention was paid to the performance of the air-cooled heat exchangers used for CPU cooling. The cooling capacity of such “heat-sink-plus-fan” (HSPF) devices was more than adequate for the vast majority of CPU applications, and the electrical power consumption of early HSPF devices was relatively low (typically on the order of 1 Watt). But eventually, increased transistor densities and higher clock speeds began to create a demand for better thermal management technology. This lead to the development of greatly improved technology for waste heat extraction, primarily practical heat pipe technology and improved thermal-interface materials. On the other hand, nearly all of the performance improvements in waste heat disposal were achieved by scaling up the size of devices based on the standard HSPF architecture; to address the problem of escalating CPU power dissipation, both the fan and the finned metal heat sink were simply made larger.
Note the distinction between “waste heat extraction” and “waste heat disposal”. As mentioned above, prior to the mid-1990s, the cooling capacity of HSPF devices was more than adequate for the vast majority of CPU applications. Typically, the main concern was creating and maintaining a low-thermal-resistance joint, which presented a challenge because the amount of surface area available for such a thermally conductive joint may be relatively small, and because the joint may be subjected to repeated thermal cycling. For this reason, the problem of thermal management has long been regarded by many as primarily a process of waste heat extraction, where in fact, thermal management also comprises a second step of waste heat disposal. In the heat extraction step, heat is removed from a high-thermal-density region such as a CPU chip and redistributed over a larger area to facilitate the second step of heat disposal, in which the waste heat is transferred to the surrounding air. The distinction between heat extraction and heat disposal, however, is often a source of confusion. For example, heat pipes, such as those used in laptop computers, may not provide any functionality with regard to heat disposal. The purpose of a heat pipe may be to extract a large quantity of heat through a small area of contact and to convey that heat to a heat exchanger, such as a finned heat sink used in conjunction with a fan, or a passive heat sink such as the metal chassis of a laptop computer. The same may be said of the thermoelectric “coolers” based on the Peltier effect, which are electrically powered heat pumps that may be used to enhance the transport of heat between a thermal load and a heat exchanger; it is the heat exchanger that ultimately performs the function of exporting substantially all of the waste heat to the surrounding air (or other thermal reservoir capable of absorbing large quantities of heat).
Of course, heat disposal may also involve transfer to water or another coolant, but for the vast majority of practical applications, the goal is to transfer waste heat to the large thermal reservoir provided by the surrounding atmosphere. With the exception of heat pipes, which can be implemented in the form of a hermetically sealed metal enclosure, there has been a great deal of reluctance to adopt cooling methodologies that entail any kind of liquid handling and/or containment. In fact, it has long been known that the thermal brick wall problem can, to a large extent, be addressed by resorting to the use of heat conducting liquids because of their superior thermal transport properties. Nonetheless, cooling systems that entail the use of liquids have not penetrated applications such as mass-marketed personal computers because of practical, rather than performance, considerations.
In recent years, the greatly increased size, weight and power consumption of air-cooled heat exchangers used for CPU cooling have begun to reach the limits of practicality for most commercial applications (most notably, mass produced personal computers for use in home and office environments). The high level of audible noise generated by the larger, more powerful fans used in high-capacity CPU coolers has also proved a deterrent to further scaling of HSPF devices (cf. Thompson, R. J. and Thompson B. F., Building the Perfect PC, O'Reilly Media, Inc., Sebastapol, Calif., 2004).
Meanwhile, progress in VLSI technology has continued. In many real-world applications, the performance of air-cooled heat exchanger technology is now the primary limiting factor to further improvements in CPU performance. Continued progress along the growth curve of Moore's Law is no longer dictated solely by improvements in VLSI technology. Because of thermal limitations, VLSI advances such as higher transistor density and the ability to operate at higher clock speeds can no longer be readily exploited.
The cooling capacity of a heat exchanger can be defined in terms of its thermal conductance, G=dP/dT, where P is the power dissipation of the thermal load, and T is the temperature of the heat exchanger at the interface between the heat exchanger and the thermal load, such that the SI unit for thermal conductance is W K−1. By convention, however, nearly all of the data sheets for CPU coolers specify performance in terms of thermal resistance, R (K W−1), the reciprocal of thermal conductance. Note that in addition to the above IUPAC (International Union of Pure and Applied Chemistry) definitions for thermal resistance and thermal conductance (cf. www.iupac.org), other names and symbols are sometimes used in the prior art to represent the same quantities (e.g., the use of the symbol “θ” for thermal resistance).
The thermal resistance of a mid-sized CPU cooler such as that shown in FIG. 1 is typically on the order of 1 K W−1. Several much larger and heavier high-capacity CPU coolers are commercially available that provide thermal resistances as low as 0.3 K W−1. But to the extent that further increases in the size, weight, and electrical power consumption of air-cooled heat sinks have become prohibitive for applications such as personal computers, efforts must now be directed at improving the three specific cooling capacity metrics for heat exchangers: cooling capacity per unit volume (W K−1 m−3), cooling capacity per unit weight (W K−1 kg−1), and cooling capacity per unit power consumption (K−1).
The essence of the “thermal brick wall” problem is that all practical options for increasing the specific capacity of devices such as CPU coolers appear to have already been exhausted. For example, steady progress over the past two decades has increased the electrical-to-mechanical efficiency of the brushless motors used in many cooling fans to a typical value of 95%. This leaves very little room for improvement. Similarly, there are thousands of references in the scientific and engineering literature on the subject of heat sink fin geometry, and optimization of the air-flow-to-heat-sink interaction. This work has resulted in a better understanding of the flow-field-heat-sink interaction, but this better understanding of the flow-field-heat-sink interaction has only led to incremental refinements in device architecture and performance.
The current state of electronics thermal management technology was summarized by DARPA (the Defense Advanced Research Projects Agency) in a January 2008 call for research proposals on new ideas for air-cooled heat exchanger technology:
“Over the past 40 years, CMOS, telecommunications, active sensing and imaging and other technologies have undergone tremendous technological innovation. Over this same historical period the technologies, designs and performance of air-cooled heat exchangers have remained unchanged. The performance data for today's state of the art heat exchangers and blowers is, in many cases, based on measurements performed in the 1960s.”
DARPA, perhaps most well known for initiating development of the Internet in the 1970s, has now decided that considerable resources must be directed towards solving the air-cooling problem (cf. www.darpa.mil/baa, DARPA Broad Agency Announcement 08-15, Jan. 8, 2008).
This technology stagnation might seem unlikely given that advances in VLSI technology have created tremendous economic incentive for improvement of air-cooled heat exchanger technology; the current market for electronics thermal management technology is ˜$5 B/yr. Part of the explanation for the lack of progress despite such large economic incentive is related to the fundamental nature of the physical effects that limit the performance of the HSPF architecture, which are discussed at length below.
The other significant contributor to technology stagnation appears to be a trend towards optimizing specific aspects of thermal management technology, rather than reconsideration of the problem as a whole. The operation of a device such a conventional CPU cooler is governed by physical processes spanning multiple engineering disciplines. As a result, an individual working on refinements to fan technology may regard a finned metal heat sink as a standardized building block that can be considered for all intents and purposes a “black box”. Likewise, an individual focused on improvement of extruded aluminum heat sink technology may regard a fan as a black box that consumes electrical power and provides airflow. Specialization in a particular area can make it very difficult to appreciate the question of optimized thermal management in its entirety. For example, one interesting observation is that the data sheets for commercially available fans used for CPU cooling rarely, if ever, provide any specification for the mechanical efficiency of the fan (i.e., the efficiency for conversion of rotary mechanical power to air flow). This is unfortunate, because as discussed below, the mechanical efficiency of the fan used in a device such as a CPU cooler turns out to have profound implications with regard to the question of overall device architecture. More generally, rethinking the problem of forced air cooling requires a reexamination of the assumptions that underlie the traditional HSPF architecture and the associated stagnation in air-cooled heat exchanger technology.
Because heat transfer is an area of fundamental technological importance, the application area for embodiments described herein is extremely broad. The preceding discussion has emphasized applications in the area of electronics cooling, where thermal management may be applied to one or more active and/or passive electronic components, including but not limited to a resistor, capacitor, inductor, transformer, diode, rectifier, thyristor, transistor, amplifier, integrated circuit, display driver, line driver, buffer, microprocessor, central processing unit, graphics processing unit, coprocessor, transducer, sensor, actuator, power supply, A.C. to D.C. converter, D.C. to A.C. converter, D.C. to D.C. converter, A.C. to A.C. converter, or printed circuit assembly. But it should be understood that embodiments described herein may be applicable to a wide variety of other technology areas (e.g., in the energy sector). Clearly, any device comprising one or more forced-air heat exchangers may benefit significantly from a reduction in the size, weight, energy consumption, and/or noise of such a heat exchanger. But in addition, the energy efficiency of such a device as a whole may be improved significantly by lowering the thermal resistance of the heat exchanger.
For example, in the energy sector, a wide variety of devices used to interconvert heat and mechanical work take the form of a heat engine sandwiched between two heat exchangers. Such a heat engine may be used to generate mechanical work from the spontaneous flow of heat from a high temperature source (hereafter referred to as a “thermal source”) to a low temperature sink (hereafter referred to as a “thermal sink”). For example, a steam turbine may generate mechanical work from spontaneous flow of heat from a thermal source, such as the combustion of fuel, to a thermal sink, such as the surrounding atmosphere. The maximum theoretical efficiency of such a heat engine is known as the Carnot efficiency, which may be expressed:
      ɛ    Carnot    =            Δ      ⁢                          ⁢      T              T      source      where T is absolute temperature, and ΔT is the difference in temperature between the thermal source and the thermal sink.
FIG. 2 illustrates a heat engine that comprises an input shaft 5 for input or output of mechanical work, a first heat exchanger 6 in thermal contact with a thermal source, and a second, identical heat exchanger 7 in thermal contact with a thermal sink. In an ideal heat engine, all of the heat that flows between the thermal source and thermal sink flows through the heat engine, there are no losses such as friction in the mechanical portion of the heat engine, the flow of heat is carried out as a reversible process, and the heat engine is thermally coupled to the thermal source and thermal sink with zero thermal resistance. In a real-world version of the heat engine shown in FIG. 2, some portion of heat transferred between the thermal source and thermal sink flows through thermal leakage paths, there are non-zero frictional losses inside the heat engine, the flow of heat must to some extent be carried out as an irreversible process to provide a reasonable rate of conversion between heat and work, and the heat exchangers that thermally couple the heat engine to the thermal source and thermal sink have finite thermal resistance. These four non-ideal effects make the actual efficiency that can be achieved in such a heat engine less than the Carnot efficiency (cf. Kittel, C. and Kroemer, H., Thermal Physics, 2nd Edition, W.H. Freeman & Company, New York, 1997). Methods by which any of these four sources of inefficiency can be substantially reduced relative to the prior art are of great technological and economic importance.
Such a heat engine may also be used as a “heat pump”, in which mechanical work is used to generate non-spontaneous flow of heat from a low temperature sink to a high temperature source. For example, a refrigerator may use mechanical work supplied by an electric motor to generate non-spontaneous flow of heat from a low temperature sink (e.g., the air inside a refrigerator) to a high temperature source (e.g., the air outside a refrigerator). The ratio of heat transferred to mechanical work supplied has a maximum theoretical value known as the Carnot coefficient of refrigerator performance:
      γ    Carnot    =            T              si        ⁢                                  ⁢        n        ⁢                                  ⁢        k                    Δ      ⁢                          ⁢      T      
To illustrate the importance of heat exchanger performance, we may consider a device such as a window-mounted air conditioner. Such a device may consist of a heat pump sandwiched between two forced-air heat exchangers. The thermal sink may be the interior room air (e.g., TSINK=300 K), and the thermal source may be the outside air on a hot summer day (e.g., TSOURCE=320 K). The two heat exchangers have a non-zero, and in this example equal, thermal resistance. During operation, a quantity of heat (q) flowing through the finite thermal resistance (R) of the two heat exchangers results in a temperature drop of qR across each heat exchanger. Under such conditions, the maximum efficiency of the heat engine is reduced to:
      γ    Carnot    =                    T                  sin          ⁢                                          ⁢          k                    -      qR                      Δ        ⁢                                  ⁢        T            +              2        ⁢        qR            where q (units: W) is the heat flux through the air conditioner and R (units: K W−1) is the heat exchanger thermal resistance. For TSINK=300 K and TSOURCE=320 K, a temperature drop of 10 K across each heat exchanger reduces the Carnot coefficient of refrigerator performance by a factor of ˜2, and may therefore increase electrical power consumption by a factor of ˜2. Accordingly, in applications such as air conditioning, where the difference in temperature between the thermal source and the thermal sink is relatively small, lowering the thermal resistance of such an air-cooled heat exchanger can reduce electrical power consumption considerably (or, for a given coefficient of performance, increase cooling capacity). Lastly, in addition to air conditioning, any such improved heat exchanger may be used for applications such as heaters, refrigerators, freezers, absorption chillers, evaporative coolers, thermal reservoirs, condensers, radiators, heat pumps, heat engines, motors, or generators.